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A classical problem in phylogenetic tree analysis is to decide whether there is a phylogenetic tree T that contains all information of a given collection P of phylogenetic trees. If the answer is “yes” we say that P is compatible and T displays P . This decision problem is NP-complete even if all input trees are quartets, that is binary trees with exactly four leaves. In this paper, we prove a ...

Phylogenetic trees are constructed frequently in biological research to provide an understanding of the evolutionary history of the organisms being studied. Often, the actual phylogenetic tree is unknown and the phylogenetic tree constructed is an estimate. There are many methods of phylogenetic tree construction which fall into two main categories: distance-based methods and character-based me...

Phylogenetic networks are a generalisation of phylogenetic trees that allow for more complex evolutionary histories that include hybridisation-like processes. It is of considerable interest whether a network can be considered ‘tree-like’ or not, which lead to the introduction of tree-based networks in the rooted, binary context. Tree-based networks are those networks which can be constructed by...

This paper focuses on tree structured data visualization. The impetus for the work will be in the domain of phylogenetic classification, which is used by the biologists to describe possible evolutionary relationships between species or individuals based on their DNA or protein sequences. It examines current tree visualization and comparison techniques and proposes a new framework that display f...

The Apiaceae family includes some of the most known medicinal, food and spice species in the world some of which have been used by humans since antiquity. Local people in different regions use many species of the family but the information regarding their uses is scattered. Traditionally used species are good candidates for bioprospecting. Combining traditional uses with phylogenetic data helps...

We present a probabilistic approach to language change in which word forms are represented by phoneme sequences that undergo stochastic edits along the branches of a phylogenetic tree. This framework combines the advantages of the classical comparative method with the robustness of corpus-based probabilistic models. We use this framework to explore the consequences of two different schemes for ...

Two trees with the same number of leaves have to be embedded in two layers in the plane such that the leaves are aligned in two adjacent layers. Additional matching edges between the leaves give a one-to-one correspondence between pairs of leaves of the different trees. Do there exist two planar embeddings of the two trees that minimize the crossings of the matching edges ? This problem has imp...

MINIMUM QUARTET INCONSISTENCY (MQI) Input: A set S of n taxa and a set QS of quartet topologies such that there is exactly one topology for every quartet set corresponding to S, and an integer k. Question: Is there an evolutionary tree T where the leaves are bijectively labeled by the elements from S such that the set of quartet topologies induced by T differs from QS in at most k quartet topol...